A13383. Same Parity Summands

You are given two positive integers $n$ ( $1 \le n \le 10^9$ ) and $k$ ( $1 \le k \le 100$ ). Represent the number $n$ as the sum of $k$ positive integers of the same parity (have the same remainder when divided by $2$ ).

In other words, find $a_1, a_2, \ldots, a_k$ such that all $a_i>0$ , $n = a_1 + a_2 + \ldots + a_k$ and either all $a_i$ are even or all $a_i$ are odd at the same time.

If such a representation does not exist, then report it.

The first line contains an integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases in the input. Next, $t$ test cases are given, one per line.

Each test case is two positive integers $n$ ( $1 \le n \le 10^9$ ) and $k$ ( $1 \le k \le 100$ ).

For each test case print:

- YES and the required values $a_i$ , if the answer exists (if there are several answers, print any of them);
- NO if the answer does not exist.

The letters in the words YES and NO can be printed in any case.